John and Rosamond want to retire in 6 years and can save $190 every three months. They plan to deposit the money at the end of each quarter into an account paying 6.48% compounded quarterly. How much will they have at the end of 6 years?
A) $5,519.62
B) $4,951.94
C) $4,126.48
D) $4,141.21
E) $6,545.91

Question

John and Rosamond want to retire in 6 years and can save $190 every three months. They plan to deposit the money at the end of each quarter into an account paying 6.48% compounded quarterly. How much will they have at the end of 6 years? ​
A) $5,519.62
B) $4,951.94
C) $4,126.48
D) $4,141.21
E) $6,545.91

Quizplus · Accepted Answer

The future value of a series formula is used to calculate the total amount accumulated over time when equal payments are made at regular intervals into an account that earns compound interest. The formula is: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $FV$ is the future value of the series, $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of payments. In this case, $P = $190$, $r = 6.48\% / 4 = 0.0162$ (since the interest is compounded quarterly), and $n = 6 \times 4 = 24$ (since there are 4 quarters in a year and the period is 6 years). Plugging these values into the formula gives the future value, which matches choice A, $5,519.62.

John and Rosamond Want to Retire in 6 Years and Can